1. If the perimeter of a square is 56 cm,
find the length of a diagonal of the
square, in simplest radical form.
2. If the diagonals of a rhombus are 6 in
and 6√5 in, find the length of a side
of the rhombus, in simplest radical
form.
3. In parallelogram ABCD, diagonals
̅̅̅̅ and 𝐵𝐷
̅̅̅̅ intersect at E. If 𝐴𝐸 =
𝐴𝐶
1
2𝑥 − 6 and 𝐶𝐸 = 𝑥 + 15, find the
2
length of AC.
4. In rectangle DEFG, diagonal 𝐷𝐹 =
20 cm and 𝐷𝐸 = 12 cm. Find the
length of DG.
5. In rhombus ABCD, diagonals ̅̅̅̅
𝐴𝐶 and ̅̅̅̅
𝐵𝐷 are
drawn. If 𝑚∠𝐵𝐴𝐶 = (2𝑥 + 10)° and
𝑚∠𝐵𝐴𝐷 = (𝑥 2 − 2𝑥 + 4)°, find 𝑥.
̅̅̅̅ & 𝑅𝑇
̅̅̅̅ are
6. In rectangle QRST, diagonals 𝑄𝑆
drawn. If 𝑚∠𝑇𝑅𝑆 = (3𝑥 − 27)° and
7
𝑚∠𝑄𝑆𝑅 = (5 𝑥 + 5)°, find 𝑚∠𝑄𝑅𝑇.
̅̅̅̅ and
7. In rhombus ABCD, diagonals 𝐴𝐶
̅̅̅̅ intersect at M. If 𝐴𝑀 = 𝑥 +
𝐵𝐷
3𝑦, 𝐵𝑀 = 𝑥 + 6, 𝑀𝐶 = 3𝑥 − 9, and
𝐷𝑀 = 2𝑦 + 8, find the value of 𝑦.
8. Find the measure of each exterior
angle of a polygon with 18 sides.
9. The measure of an exterior angle of a
regular polygon is 36°. Find the
number of sides of the polygon
10. How many sides does a regular
polygon have if each interior angle
measures 160°?
11. The sum of the interior angles of a
regular polygon measure 1980°, how
many sides does the polygon have?
12.Find the value of x:
13.Find the value of x:
14.Find the value of x:
15.Find the value of x:
16.Find 𝑚∠𝐶𝐷𝐵.
̅̅̅̅
17.Rectangle GALS has diagonals 𝐺𝐿
̅̅̅̅. If 𝐺𝐿 = 3𝑎 + 6 and 𝐴𝑆 =
and 𝐴𝑆
5𝑎 − 18, then 𝑎 =?
18.In the rectangle RAIN below, YR =
3x and NY = 18, find ‘x’
19.𝑚∠3 = 110°. Find the measure of
∠1.
20.If 𝑚∠𝐷𝐴𝐶 = 2𝑥 + 4 and 𝑚∠𝐵𝐴𝐶 =
3𝑥 + 1, find 𝑥.
21.If 𝑅𝑇 = 5𝑥 + 8 and 𝑅𝑍 = 4𝑥 + 1,
find 𝑍𝑇.
22.If 𝐴𝐵 = 2𝑥 + 4 and 𝐶𝐷 = 3𝑥 − 5,
find 𝐵𝐷.
23.The area of the square is 16. Find
EC.
24.ACKJ is a rhombus. 𝐴𝐶 = 6𝑦 + 4,
𝐶𝐾 = 5𝑦 + 8, and 𝐾𝐽 = 3𝑦 + 16.
Find the value of ‘y’.
25.Quadrilateral DKLM is a rhombus. If
𝐷𝐴 = 4𝑥 and 𝐴𝐿 = 5𝑥 − 3, find DL.
26.Find the measure of angle 1, 2, 3,
and 4 in the following rhombus (hint:
they are all the same)
27.WXYZ is a square. If WT = 3, find ZX.
28.WXYZ is a square. If WT = 3, find XY.
29.WXYZ is a square. If WT = 3, find
𝑚∠𝑊𝑌𝑋.
30. Which quadrilaterals always have
consecutive angles that are
supplementary? (Check all that
apply)